Convergence Analysis of an Accelerated Iteration for Monotone Generalized α-Nonexpansive Mappings with a Partial Order

In this paper, we introduce a new accelerated iteration for finding a fixed point of monotone generalized α-nonexpansive mapping in an ordered Banach space. We establish some weak and strong convergence theorems of fixed point for monotone generalized α-nonexpansive mapping in a uniformly convex Ban...

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Bibliographic Details
Published in:Journal of function spaces 2019-01, Vol.2019 (2019), p.1-8
Main Authors: Chen, Yi-An, Wen, Dao-Jun
Format: Article
Language:English
Subjects:
Banach spaces
Convergence
Fixed points (mathematics)
Iterative methods
Mapping
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Summary:In this paper, we introduce a new accelerated iteration for finding a fixed point of monotone generalized α-nonexpansive mapping in an ordered Banach space. We establish some weak and strong convergence theorems of fixed point for monotone generalized α-nonexpansive mapping in a uniformly convex Banach space with a partial order. Further, we provide a numerical example to illustrate the convergence behavior and effectiveness of the proposed iteration process.
ISSN:2314-8896
2314-8888
DOI:10.1155/2019/2789819